1 8 Solving Applied Problems Involving Whole Numbers

Problem Solving Steps 1. Understand the problem. a) b) c) 2. Solve and state the answer. a) b) 3. Read the problem carefully. Draw a picture if this is helpful. Fill in the Mathematics Blueprint so that you have the facts and a method of proceeding in this situation. Perform the calculations. State the answer, including the unit of measure. Check. a) b) Estimate the answer. Compare the exact answer with the estimate to see if your answer is reasonable. Tobey & Slater, Basic College Mathematics, 6 e 2

Mathematics Blueprint The Mathematical Blueprint is simply a sheet of paper with four columns. Each column tells you something to do. Mathematics Blueprint for Problem Solving Gather the Facts What Am I Asked to Do? How Do I Proceed? Tobey & Slater, Basic College Mathematics, 6 e Key Points to Remember 3

Problems Involving One Type of Operation Example: There are 144 pencils in a gross. Mr. Weston ordered 14 gross of pencils for the office. How many pencils did he order? Mathematics Blueprint for Problem Solving Gather the Facts What Am I Asked to Do? How Do I Proceed? There are 144 pencils in a gross. 14 gross were ordered. Find the total I need to number of multiply 144 by pencils Mr. 14. Weston ordered. Key Points to Remember It does not matter that Mr. Weston ordered the pencils for the office. 144 14 = 2016 Mr. Weston ordered 2016 pencils. Tobey & Slater, Basic College Mathematics, 6 e 4

Problems Involving Two Types of Operations Example: Juanita bought six bath towels for $15 each, eight washcloths for $7 each, and three bathroom rugs for $20 each for her new bathroom. What was the total cost of these items? Mathematics Blueprint for Problem Solving Gather the Facts What Am I Asked to Do? six towels at Find the total $15 each, eight cost of all of washcloths at these items. $7 each, three rugs at $20 each How Do I Proceed? Key Points to Remember I need to multiply 6 by 15; 8 by 7; and 3 by 20. Then I need to add these products. I need to multiply first, and then add to find the total cost. Example continues. Tobey & Slater, Basic College Mathematics, 6 e 5

Problems Involving Two Types of Operations Example continued Mathematics Blueprint for Problem Solving Gather the Facts What Am I Asked to Do? six towels at Find the total $15 each, eight cost of all of washcloths at these items. $7 each, three rugs at $20 each 6 15 = 90 8 7 = 56 3 20 = 60 How Do I Proceed? Key Points to Remember I need to multiply 6 by 15; 8 by 7; and 3 by 20. Then I need to add these products. I need to multiply first, and then add to find the total cost. 90 + 56 + 60 = 206 Juanita’s total cost for these items was $206. Tobey & Slater, Basic College Mathematics, 6 e 6